Cluster analysis plays an indispensable role in machine learning and data mining. Learning a good data representation is crucial for clustering algorithms. Recently, deep clustering (DC), which can learn clustering-friendly representations using deep neural networks (DNNs), has been broadly applied in a wide range of clustering tasks. Existing surveys for DC mainly focus on the single-view fields and the network architectures, ignoring the complex application scenarios of clustering. To address this issue, in this article, we provide a comprehensive survey for DC in views of data sources. With different data sources, we systematically distinguish the clustering methods in terms of methodology, prior knowledge, and architecture. Concretely, DC methods are introduced according to four categories, i.e., traditional single-view DC, semi-supervised DC, deep multiview clustering (MVC), and deep transfer clustering. Finally, we discuss the open challenges and potential future opportunities in different fields of DC.

In recent years, incomplete multi-view clustering (IMVC), which studies the challenging multi-view clustering problem on missing views, has received growing research interests. Previous IMVC methods suffer from the following issues: (1) the inaccurate imputation for missing data, which leads to suboptimal clustering performance, and (2) most existing IMVC models merely consider the explicit presence of graph structure in data, ignoring the fact that latent graphs of different views also provide valuable information for the clustering task. To overcome such challenges, we present a novel method, termed Adaptive feature imputation with latent graph for incomplete multi-view clustering (AGDIMC). Specifically, it captures the embbedded features of each view by incorporating the view-specific deep encoders. Then, we construct partial latent graphs on complete data, which can consolidate the intrinsic relationships within each view while preserving the topological information. With the aim of estimating the missing sample based on the available information, we utilize an adaptive imputation layer to impute the embedded feature of missing data by using cross-view soft cluster assignments and global cluster centroids. As the imputation progresses, the portion of complete data increases, contributing to enhancing the discriminative information contained in global pseudo-labels. Meanwhile, to alleviate the negative impact caused by inferior impute samples and the discrepancy of cluster structures, we further design an adaptive imputation strategy based on the global pseudo-label and the local cluster assignment. Experimental results on multiple real-world datasets demonstrate the effectiveness of our method over existing approaches.

Deep multi-view subspace clustering (DMVSC) has recently attracted increasing attention due to its promising performance. However, existing DMVSC methods still have two issues: (1) they mainly focus on using autoencoders to nonlinearly embed the data, while the embedding may be suboptimal for clustering because the clustering objective is rarely considered in autoencoders, and (2) existing methods typically have a quadratic or even cubic complexity, which makes it challenging to deal with large-scale data. To address these issues, in this paper we propose a novel deep multi-view subspace clustering method with anchor graph (DMCAG). To be specific, DMCAG firstly learns the embedded features for each view independently, which are used to obtain the subspace representations. To significantly reduce the complexity, we construct an anchor graph with small size for each view. Then, spectral clustering is performed on an integrated anchor graph to obtain pseudo-labels. To overcome the negative impact caused by suboptimal embedded features, we use pseudo-labels to refine the embedding process to make it more suitable for the clustering task. Pseudo-labels and embedded features are updated alternately. Furthermore, we design a strategy to keep the consistency of the labels based on contrastive learning to enhance the clustering performance. Empirical studies on real-world datasets show that our method achieves superior clustering performance over other state-of-the-art methods.

Multi-view clustering (MVC) is a popular technique for improving clustering performance using various data sources. However, existing methods primarily focus on acquiring consistent information while often neglecting the issue of redundancy across multiple views. This study presents a new approach called Sufficient Multi-View Clustering (SUMVC) that examines the multi-view clustering framework from an information-theoretic standpoint. Our proposed method consists of two parts. Firstly, we develop a simple and reliable multi-view clustering method SCMVC (simple consistent multi-view clustering) that employs variational analysis to generate consistent information. Secondly, we propose a sufficient representation lower bound to enhance consistent information and minimise unnecessary information among views. The proposed SUMVC method offers a promising solution to the problem of multi-view clustering and provides a new perspective for analyzing multi-view data. To verify the effectiveness of our model, we conducted a theoretical analysis based on the Bayes Error Rate, and experiments on multiple multi-view datasets demonstrate the superior performance of SUMVC.